Kepler S Third Law Of Planetary Motion Equation

The sun and the planet are separated by distance r.

Kepler s third law of planetary motion equation. Mass of the earth 5 98x10 24 kg t 2 35x10 6 s g 6 6726 x 10 11 n m 2 kg 2. Kepler proposed the first two laws in 1609 and the third in 1619 but it was not until the 1680s that isaac newton explained why planets follow these laws. Thus we find that mercury the innermost planet takes only 88 days to orbit the sun but the outermost planet pluto requires 248 years to do the same. Kepler s third law states that the square of the period is proportional to the cube of the semi major axis of the orbit.

The law of orbits. A derivation of kepler s third law of planetary motion is a standard topic in engineering mechanics classes. All planets move in elliptical orbits with the sun at one focus. Newton showed that kepler s laws were a consequence of both his laws of motion and his law of gravitation.

Johannes kepler working with data painstakingly collected by tycho brahe without the aid of a telescope developed three laws which described the motion of the planets across the sky. With the help of. Determine the radius of the moon s orbit. Kepler s third law sometimes referred to as the law of harmonies compares the orbital period and radius of orbit of a planet to those of other planets.

Substitute the values in the below satellite mean orbital radius equation. The period of the moon is approximately 27 2 days 2 35x10 6 s. Murray and dermott solar system dynamics cambridge university press 1999 isbn 0 521 57597 4. Kepler s third law implies that the period for a planet to orbit the sun increases rapidly with the radius of its orbit.

Unlike kepler s first and second laws that describe the motion characteristics of a single planet the third law makes a comparison between the motion characteristics of different planets. See for example pages 161 164 of meriam j l. Also known as the law of harmonies kepler s third law of planetary motion states that the square of the orbital period represented as t of a planet is directly proportional to the cube of the average distance or the semi major axis of the orbit represented as r of a planet from the sun. Consider a planet of mass is moving in an elliptical orbit around the sun.

Kepler s third law examples. In satellite orbits and energy we derived kepler s third law for the special case of a circular orbit. Equation 13 8 gives us the period of a circular orbit of radius r about earth.